Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 May 25 2022 11:49:25
%S 1,1,2,2,3,4,5,6,7,10,10,13,16,18,21,24,31,31,38,44,49,56,62,76,76,90,
%T 100,113,126,136,161,161,186,201,234,252,267,308,308,349,370,449,462,
%U 483,546,546,609,637,813,792
%N Number of partitions of n into parts that are distinct mod 7.
%H Fausto A. C. Cariboni, <a href="/A114095/b114095.txt">Table of n, a(n) for n = 1..1000</a>
%e a(7)=5 because there are 5 such partitions of 7: {7}, {1,6}, {2,5}, {3,4}, {4,2,1}.
%t << DiscreteMath`Combinatorica`; np[n_]:= Length@Select[Mod[ #,7]& /@ Partitions[n],(Length@# == Length@Union@#)&]; lst = Array[np,50] (* corrected by _Seth A. Troisi_, May 17 2022 *)
%o (PARI) a(n) = my(nb=0); forpart(p=n, if (#p == #Set(apply(x->(x%7), Vec(p))), nb++)); nb; \\ _Michel Marcus_, May 18 2022
%K nonn
%O 1,3
%A _Giovanni Resta_, Feb 06 2006